Seriously... the hallmark of all the linear algebra classes I had was the instructor completely failing to demonstrate the various concepts in visual terms. And that's pretty unforgivable, since linear algebra feels like one of those subjects where, until you have some key components of it modeled in your head that serve to glue everything together, every new may as well be random words pulled from a foreign dictionary.

Some of this comes down to learning-style. It sounds like your lecturer was not a visual thinker. Some people really like to just get the algebra and have-at-it (not me tho.) The "model" you refer to doesn't need to be visual. There are applications of linear algebra where the visual stuff just doesn't help much.